Given f''(x) find f'(x) and f(x).

Question

f''(x)=cos(x), f'(pi/2)=7 and f(pi/2)=3

Answer 1

First, find the general equation of f'(x) and f(x).

 

f'(x) = sin(x) + C

 

f(x) = -cos(x) + Cx + D

 

 

Set f'(π/2)=7        to solve for C.

 

1 + C = 7

 

      C = 6

 

Plug in this value of C into f(x) and use the other condition to solve for D.

 

-cos(π/2) + 6x + D = 3

 

6(π/2) + D = 3

 

3π + D = 3

 

        D = 3 - 3π

 

 

f'(x) = sin(x) + 6

 

f(x) = -cos(x) + 6x + 3 - 3π